From 6e475df77ad66c36ac3405cb553f5de0e64a94e5 Mon Sep 17 00:00:00 2001
From: zleyyij <75810274+zleyyij@users.noreply.github.com>
Date: Wed, 18 Sep 2024 12:12:12 -0600
Subject: [PATCH] vault backup: 2024-09-18 12:12:12
---
education/math/MATH1060 (trig)/Identities.md | 20 ++++++++++++++------
1 file changed, 14 insertions(+), 6 deletions(-)
diff --git a/education/math/MATH1060 (trig)/Identities.md b/education/math/MATH1060 (trig)/Identities.md
index 1382000..827001f 100644
--- a/education/math/MATH1060 (trig)/Identities.md
+++ b/education/math/MATH1060 (trig)/Identities.md
@@ -5,15 +5,23 @@ All of the following only apply when the denominator is not equal to zero.
$$ tan \theta = \frac{y}{x} $$
Because the following are inverses of their counterparts, you only need to remember the equivalents for $sin$, $cos$, and $tan$, then just find the inverse by taking $1/v$.
-| Base Identity | Inverse Identity | Alternate Identities | Alternate Inverse Identities |
-| ----------------------------- | ------------------------------ | --------------------------------------------- | ------------------------------------------------------------------------- |
-| $$ sin\theta = y $$ | $$ csc\theta = \frac{1}{y} $$ | | $$ csc\theta = \frac{1}{sin\theta} $$ |
-| $$ cos\theta = x $$ | $$ sec \theta = \frac{1}{x} $$ | | |
-| $$ tan\theta = \frac{y}{x} $$ | $$ cot\theta = \frac{x}{y} $$ | $$ tan\theta = \frac{sin\theta}{cos\theta} $$ | <br>$$ cot\theta = \frac{1}{tan\theta} = \frac{cos\theta}{sin{\theta}} $$ |
-| | | | |
+| Base Identity | Inverse Identity | Alternate Identities | Alternate Inverse Identities |
+| ----------------------------- | ------------------------------ | --------------------------------------------- | --------------------------------------------------------------------- |
+| $$ sin\theta = y $$ | $$ csc\theta = \frac{1}{y} $$ | | $$ csc\theta = \frac{1}{sin\theta} $$ |
+| $$ cos\theta = x $$ | $$ sec \theta = \frac{1}{x} $$ | | $$ sec\theta = \frac{1}{cos\theta} $$ |
+| $$ tan\theta = \frac{y}{x} $$ | $$ cot\theta = \frac{x}{y} $$ | $$ tan\theta = \frac{sin\theta}{cos\theta} $$ | $$ cot\theta = \frac{1}{tan\theta} = \frac{cos\theta}{sin{\theta}} $$ |
+
$$ cot \theta = \frac{x}{y} $$
$$ sec\theta = \frac{1}{cos\theta}$$
$$ csc\theta = \frac{1}{sin\theta}$$
# Pythagorean Identities
The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
$$ sin^2 \theta + cos^2 \theta = 1 $$
+There are more forms that are useful, but they can be derived from the above formula:
+$$ 1 + tan^2\theta = sec^2\theta $$
+$$ cot^2 \theta + 1 = csc^2\theta $$
+# Even and Odd Identities
+- A function is even if $f(-x) = f(x)$.
+- A function is odd if $f(-x) = -f(x)$
+Cosine and secant are **even*
+## Examples